Some one has done the comparison. https://cameradecision.com/compare/Panasonic-Lumix-DC-S1-vs-Olympus-OM-D-E-M1X
As always, based on individual point of view and personal like + dislike. YMMV.
One look at the article photo and you get this impression. The EM1X sensor is smaller and yet the camera body is bigger and heavier.
If you like the particular look of photos from Leica lenses that the S1 can use, then it is a deciding factor.
But to be fair to Olympus, that is each individual's personal choice.
Have heard from a friend that EM1X has long battery life, has a 2x crop factor (meaning long telephoto), is weather proof, has high speed sequential shooting, has hybrid phase and contrast detect autofocus, has dual UHS-II slots - all of which makes it good to use in bird shooting.
I would rather go with the S1 because the future of the mount is more certain, but I would wait until the second generation arrives. At the moment, Nikon Z6 is also one I would consider because the lens mount is so different that it will be better into the future than the others.
The E-M1x would be useful, but I would prefer to go with the Panasonic G9, if I'm sticking with micro Four-Thirds.